Frequency domain singular spectrum analysis: an application to climate time series decomposition

This paper proposes an adaptation of Singular Spectrum Analysis (SSA) for time series decomposition, denoted Frequency Domain SSA (FDSSA), and compares its performance with Classic SSA and traditional TRAMO-SEATS and X13-ARIMA decomposition methods. Unlike these two last well known methods, which rely on ARIMA models and predefined moving averages, SSA allows for the extraction of components such as trend, seasonality, and irregularity without imposing rigid statistical assumptions. From a methodological standpoint, this study incorporates a semi-automatic procedure based on frequency domain criteria into the grouping step. As an empirical application, three monthly climate time series from the city of Bilbao between 2002 and 2023 are analysed: accumulated precipitation, average temperature, and average wind speed. The spectral density function of the different components and the gain of the filters are used to compare and evaluate the results obtained with different techniques. The FDSSA provides greater flexibility in signal extraction, detecting trends that remain hidden with other traditional signal extraction techniques and important harmonics associated with seasonality. Overall, this work highlights the potential of FDSSA as a robust methodological tool for component analysis in time series.